63.20.2 problem 2(b)

Internal problem ID [13224]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 218
Problem number : 2(b)
Date solved : Tuesday, January 28, 2025 at 05:12:40 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x\\ y^{\prime }\left (t \right )&=3 x-4 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 23

dsolve([diff(x(t),t)=x(t),diff(y(t),t)=3*x(t)-4*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ y &= \frac {3 c_{2} {\mathrm e}^{t}}{5}+{\mathrm e}^{-4 t} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 149

DSolve[{D[x[t],t]==x[t]+y[t],D[y[t],t]==3*x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{74} e^{-\frac {1}{2} \left (3+\sqrt {37}\right ) t} \left (c_1 \left (\left (37+5 \sqrt {37}\right ) e^{\sqrt {37} t}+37-5 \sqrt {37}\right )+2 \sqrt {37} c_2 \left (e^{\sqrt {37} t}-1\right )\right ) \\ y(t)\to \frac {1}{74} e^{-\frac {1}{2} \left (3+\sqrt {37}\right ) t} \left (6 \sqrt {37} c_1 \left (e^{\sqrt {37} t}-1\right )-c_2 \left (\left (5 \sqrt {37}-37\right ) e^{\sqrt {37} t}-37-5 \sqrt {37}\right )\right ) \\ \end{align*}